Finding Terms
Maths: Edexcel IGCSE Higher, topic 3.1.2
Sequences
Is 30 part of the sequence given by the expression n² + 5? What about 40?
Write out the formula with answer 30
Solve for n
We find n = ± 5
- n can only be positive so discard the negative answer.
5 is an integer so 30 is in the sequence
Write out the formula with answer 40
Solve for n
We find n = ± 5.91...
- n can only be positive so discard the negative answer.
5.91... is not an integer so 40 is not part of the sequence
Arithmetic Sequence
Terms in arithmetic sequences change by a constant amount each time.
Arithmetic sequence
- An arithmetic sequence is a sequence that has the property that the difference between any two consecutive terms is a constant.
- This difference is called the common difference, and is represented by the symbol d.
Nth term
- Given the first term and the common difference of an arithmetic sequence, we can find the nth term of the sequence an by using the following equation:
- Where n ≥ 2.
Finding the Sum of Sequences
It is often useful to find the sum of the terms in a sequence.
Notation
- The sum of the first n terms of a sequence Sn is written as:
- Sn = a1 for all sequences.
Sum of first n terms
- The equation for Sn is:
Test yourself on Finding Terms
Is 62 in the sequence n² - 2
Is 45 in the sequence n² + 3
Is 22 in the sequence n² + 8
What is the sum of the first 3 terms of the following sequence?
4, 6, 8, 10, ...What is the sum of the first 4 terms of the following sequence?
4, 6, 8, 10, ...